# Applied Optimization For Wireless, Machine Learning, Big Data

- Institution: IIT Kanpur
- Department: Electrical Engineering
- Teacher: Prof. Aditya K. Jagannatham
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108104112)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108104112)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 01- Vectors and Matrices- Linear Independence and Rank](https://invisiblenetwork.ai/learn/nptel/108104112/36936c97dee7) (Video)
2. [Lec 02 - Eigenvectors and Eigenvalues of Matrices and their Properties](https://invisiblenetwork.ai/learn/nptel/108104112/97cb4a2e040e) (Video)
3. [Lec 03 - Positive Semidefinite (PSD) and Postive Definite (PD) Matrices and their Properties](https://invisiblenetwork.ai/learn/nptel/108104112/58ec97f60152) (Video)
4. [Lec 04 - Inner Product Space and it's Properties: Linearity, Symmetry and Positive Semi-definite](https://invisiblenetwork.ai/learn/nptel/108104112/908bcbb95f03) (Video)
5. [Lec 05 - Inner Product Space and its Properties: Cauchy Schwarz Inequality](https://invisiblenetwork.ai/learn/nptel/108104112/2e23b1b80da0) (Video)
6. [Lec 06 - Properties of Norm, Gaussian Elimination and Echleon form of matrix](https://invisiblenetwork.ai/learn/nptel/108104112/0c26ffc8970a) (Video)
7. [Lec 07- Gram Schmidt Orthogonalization Procedure](https://invisiblenetwork.ai/learn/nptel/108104112/76316140e591) (Video)
8. [Lec 08- Null Space and Trace of Matrices](https://invisiblenetwork.ai/learn/nptel/108104112/69e601736c0d) (Video)
9. [Lec 09- Eigenvalue Decomposition of Hermitian Matrices and Properties](https://invisiblenetwork.ai/learn/nptel/108104112/6f585e0f226e) (Video)
10. [Lec 10- Matrix Inversion Lemma (Woodbury identity)](https://invisiblenetwork.ai/learn/nptel/108104112/8c7697ac4cd6) (Video)
11. [Lec 11- Introduction to Convex Sets and Properties](https://invisiblenetwork.ai/learn/nptel/108104112/d8de98c7d342) (Video)
12. [Lec 12- Affine Set Examples and Application](https://invisiblenetwork.ai/learn/nptel/108104112/46f733f2ad53) (Video)
13. [Lec 13- Norm Ball and its Practical Applications](https://invisiblenetwork.ai/learn/nptel/108104112/3c5fbe1cf672) (Video)
14. [Lec 14- Ellipsoid and its Practical Applications](https://invisiblenetwork.ai/learn/nptel/108104112/9f4b520ec53b) (Video)
15. [Lec 15- Norm Cone,Polyhedron and its Applications](https://invisiblenetwork.ai/learn/nptel/108104112/8c84acd6f1ee) (Video)
16. [Lec 16- Applications: Cooperative Cellular Transmission](https://invisiblenetwork.ai/learn/nptel/108104112/0d06680da62d) (Video)
17. [Lec 17- Positive Semi Definite Cone And Positive Semi Definite (PSD) Matrices](https://invisiblenetwork.ai/learn/nptel/108104112/e5bdf96b96a5) (Video)
18. [Lec 18-Introduction to Affine functions and examples](https://invisiblenetwork.ai/learn/nptel/108104112/dfefc5ec4abc) (Video)
19. [Lecture 19-norm balls and Matrix properties:Trace,Determinant](https://invisiblenetwork.ai/learn/nptel/108104112/5ef2117684c3) (Video)
20. [Lecture 20-Inverse of a Positive Definite Matrix](https://invisiblenetwork.ai/learn/nptel/108104112/db52a15c3d1e) (Video)
21. [Lecture 21-Example Problems: Property of Norms,Problems on Convex Sets](https://invisiblenetwork.ai/learn/nptel/108104112/c5532472d7bf) (Video)
22. [Lecture 22-Problems on Convex Sets(contd.)](https://invisiblenetwork.ai/learn/nptel/108104112/f61fc3b4c573) (Video)
23. [Lecture 23-Introduction to Convex and Concave Functions](https://invisiblenetwork.ai/learn/nptel/108104112/67caacbb772a) (Video)
24. [Lecture 24-Properties of Convex Functions with examples](https://invisiblenetwork.ai/learn/nptel/108104112/7a4631e9e6e6) (Video)
25. [Lec 25-Test for Convexity: Positive Semidefinite Hessian Matrix](https://invisiblenetwork.ai/learn/nptel/108104112/b3439c96472a) (Video)
26. [Lec 26-Application: MIMO Receiver Design as a Least Squares Problem](https://invisiblenetwork.ai/learn/nptel/108104112/30abd4510380) (Video)
27. [Lec 27-Jensen's Inequality and Practical Application](https://invisiblenetwork.ai/learn/nptel/108104112/9e99e84f6794) (Video)
28. [Lec 28-Jensen's Inequality application](https://invisiblenetwork.ai/learn/nptel/108104112/50e02e14fe6e) (Video)
29. [Lec 29 - Properties of Convex Functions](https://invisiblenetwork.ai/learn/nptel/108104112/604a49a49df0) (Video)
30. [Lec 30 - Conjugate Function and Examples to prove Convexity of various Functions](https://invisiblenetwork.ai/learn/nptel/108104112/1fe08e3ca5e5) (Video)
31. [Lec 31- Example problems: Operations preserving Convexity(log-sum, average) and Quasi Convexity](https://invisiblenetwork.ai/learn/nptel/108104112/f773e781a7b8) (Video)
32. [Lec 32-Example Problems: Verify Convexity, Quasi -Convexity and Quasi- Concavity of functions](https://invisiblenetwork.ai/learn/nptel/108104112/8932e09c3f23) (Video)
33. [Lec 33-Example Problems:Perspective function, Product of Convex functions and Pointwise Maximum is Convex](https://invisiblenetwork.ai/learn/nptel/108104112/3c1e789d4f63) (Video)
34. [Lec 34- Practical Application: Beamforming in Multi-antenna Wireless Communication](https://invisiblenetwork.ai/learn/nptel/108104112/a0c523f5852a) (Video)
35. [Lec 35 - Practical Application: Maximal Ratio Combiner for Wireless Systems](https://invisiblenetwork.ai/learn/nptel/108104112/c617d03f0147) (Video)
36. [Lec 36- Practical Application: Multi-antenna Beamforming with Interfering User](https://invisiblenetwork.ai/learn/nptel/108104112/860fea976067) (Video)
37. [Lec 37- Practical Application: Zero-Forcing (ZF) Beamforming with Interfering User](https://invisiblenetwork.ai/learn/nptel/108104112/6f09d179fd36) (Video)
38. [Lec 38- Practical Application: Robust Beamforming With Channel Uncertainity for Wireless Systems](https://invisiblenetwork.ai/learn/nptel/108104112/822334ab0414) (Video)
39. [Lec 39- Practical Application: Robust Beamformer Design for Wireless Systems](https://invisiblenetwork.ai/learn/nptel/108104112/76fef3d5aa3e) (Video)
40. [Lec 40 - Practical Application: Detailed Solution for Robust Beamformer Computation in Wireless Systems Text](https://invisiblenetwork.ai/learn/nptel/108104112/f17305e2d477) (Video)
41. [Lec 41- Linear modeling and Approximation Problems: Least Squares](https://invisiblenetwork.ai/learn/nptel/108104112/931c5c4e713e) (Video)
42. [Lec 42-Geometric Intuition for Least Squares](https://invisiblenetwork.ai/learn/nptel/108104112/5b5a6c7a6b75) (Video)
43. [Lec 43- Practical Application: Multi antenna channel estimation](https://invisiblenetwork.ai/learn/nptel/108104112/1d1b291de5da) (Video)
44. [Lec 44- Practical Application:Image deblurring](https://invisiblenetwork.ai/learn/nptel/108104112/a624d646d0e6) (Video)
45. [Lec 45- Least Norm Signal Estimation](https://invisiblenetwork.ai/learn/nptel/108104112/d981969f7b24) (Video)
46. [Lec 46- Regularization: Least Squares + Least Norm](https://invisiblenetwork.ai/learn/nptel/108104112/78f4a8053029) (Video)
47. [Lec 47- Convex Optimization Problem representation: Canonical form, Epigraph form](https://invisiblenetwork.ai/learn/nptel/108104112/942764a9ee5d) (Video)
48. [Lec 48-Linear Program Practical Application: Base Station Co-operation](https://invisiblenetwork.ai/learn/nptel/108104112/f41e17191010) (Video)
49. [Lec 49- Stochastic Linear Program,Gaussian Uncertainty](https://invisiblenetwork.ai/learn/nptel/108104112/8a889f57f3f9) (Video)
50. [Lec 50- Practical Application: Multiple Input Multiple Output (MIMO) Beamforming](https://invisiblenetwork.ai/learn/nptel/108104112/ac4a06b5f43e) (Video)
51. [Lec 51- Practical Application: Multiple Input Multiple Output (MIMO) Beamformer Design](https://invisiblenetwork.ai/learn/nptel/108104112/7262c2ae3208) (Video)
52. [Lec 52-Practical Application: Co-operative Communication, Overview and various Protocols used](https://invisiblenetwork.ai/learn/nptel/108104112/fd7bfe3e0543) (Video)
53. [Lec 53- Practical Application: Probability of Error Computation for Co-operative Communication](https://invisiblenetwork.ai/learn/nptel/108104112/f5db0cc52eb2) (Video)
54. [Lec 54- Practical Application:Optimal power allocation factor determination for Co-operative Communication](https://invisiblenetwork.ai/learn/nptel/108104112/36e7bf8063dc) (Video)
55. [Lec 55- Practical Application: Compressive Sensing](https://invisiblenetwork.ai/learn/nptel/108104112/991674d3d3f3) (Video)
56. [Lec 56- Practical Application](https://invisiblenetwork.ai/learn/nptel/108104112/7aa7623b20d3) (Video)
57. [Lec 57- Practical Application- Orthogonal Matching Pursuit (OMP) algorithm for Compressive Sensing](https://invisiblenetwork.ai/learn/nptel/108104112/f04a4fbf2e5e) (Video)
58. [Lec 58- Example Problem: Orthogonal Matching Pursuit (OMP) algorithm](https://invisiblenetwork.ai/learn/nptel/108104112/7234fdd41132) (Video)
59. [Lec 59- Practical Application : L1 norm minimization and regularization approach for Compressive Sensing Optimization problem](https://invisiblenetwork.ai/learn/nptel/108104112/f827b5789d0d) (Video)
60. [Lec 60- Practical Application of Machine Learning and Artificial Intelligence:Linear Classification, Overview and Motivation](https://invisiblenetwork.ai/learn/nptel/108104112/c62020426cb3) (Video)
61. [Lec 61- Practical Application: Linear Classifier (Support Vector Machine) Design](https://invisiblenetwork.ai/learn/nptel/108104112/1cf9ca189847) (Video)
62. [Lec 62- Practical Application: Approximate Classifier Design](https://invisiblenetwork.ai/learn/nptel/108104112/9c9348d670aa) (Video)
63. [Lec 63- Concept of Duality](https://invisiblenetwork.ai/learn/nptel/108104112/0ccb2f424beb) (Video)
64. [Lec 64-Relation between optimal value of Primal & Dual Problems, concepts of Duality gap and Strong Duality](https://invisiblenetwork.ai/learn/nptel/108104112/c760744c9a36) (Video)
65. [Lec 65-Example problem on Strong Duality](https://invisiblenetwork.ai/learn/nptel/108104112/ebd627e3c7ff) (Video)
66. [Lec 66- Karush-Kuhn-Tucker(KKT) conditions](https://invisiblenetwork.ai/learn/nptel/108104112/71625e5338f9) (Video)
67. [Lec 67- Application of KKT condition:Optimal MIMO power allocation(Waterfilling)](https://invisiblenetwork.ai/learn/nptel/108104112/2ca91e02dac0) (Video)
68. [Lec 68- Optimal MIMO Power allocation(Waterfilling)-II](https://invisiblenetwork.ai/learn/nptel/108104112/d5adeb048287) (Video)
69. [Lec 69- Example problem on Optimal MIMO Power allocation(Waterfilling)](https://invisiblenetwork.ai/learn/nptel/108104112/9c577dd0a16f) (Video)
70. [Lec 70- Linear objective with box constraints, Linear Programming](https://invisiblenetwork.ai/learn/nptel/108104112/16cdee0fb2dd) (Video)
71. [Lec 71- Example Problems II](https://invisiblenetwork.ai/learn/nptel/108104112/240bad3aa4bf) (Video)
72. [Lec 72- Examples on Quadratic Optimization](https://invisiblenetwork.ai/learn/nptel/108104112/f5b50a86d3b6) (Video)
73. [Lec 73- Examples on Duality: Dual Norm, Dual of Linear Program(LP)](https://invisiblenetwork.ai/learn/nptel/108104112/c019cd51e2bd) (Video)
74. [Lec 74- Examples on Duality: Min-Max problem, Analytic Centering](https://invisiblenetwork.ai/learn/nptel/108104112/e1c4ba286bc6) (Video)
75. [Lec 75- Semi Definite Program(SDP) and its application:MIMO symbol vector decoding](https://invisiblenetwork.ai/learn/nptel/108104112/2bdf2a49e027) (Video)
76. [Lec 76- Application:SDP for MIMO Maximum Likelihood(ML) Detection](https://invisiblenetwork.ai/learn/nptel/108104112/674518f4ee3a) (Video)
77. [Lec 77- Introduction to big Data: Online Recommender System(Netflix)](https://invisiblenetwork.ai/learn/nptel/108104112/73767c2f6c6b) (Video)
78. [Lec 78- Matrix Completion Problem in Big Data: Netflix-I](https://invisiblenetwork.ai/learn/nptel/108104112/6cc0506b0f65) (Video)
79. [Lec 79- Matrix Completion Problem in Big Data: Netflix-II](https://invisiblenetwork.ai/learn/nptel/108104112/1d4897cb2f29) (Video)